Abstract
In the present study, we investigate solitary wave solutions to the Drinfeld-Sokolov system. This system describes the dispersive water waves in fluid mechanics and is known as an anisotropic integrable system along with a Lax extension of the famous Korteweg-De Vries equation. The pivotal aim of this study is to make much more contributions to the fluid mechanics by extracting various versions of traveling waves which are helpful to further understand the mechanism of propagation of the dispersive waves. The presented method used for achieving our main goal is the generalized exponential rational function method. Several different categories of solutions are all determined using a single structure in the utilized technique. After comparing with the existing methods, such as the Exp-function method, the generated exact wave solutions show the efficiency of the utilized method. For the sake of discovering more facts about the numerical nature of obtained wave solutions, several 2D diagrams have been shown. Further, the acquired results of this paper also pave the way for the use of the technique in solving other nonlinear models.